Methods, systems and devices for modelling reservoir properties

ABSTRACT

Aspects of the present disclosure may provide devices, systems and methods for modelling resource production for which there may be incomplete information and/or unknown parameters. In some embodiments, the method includes applying an analytical fracture model and reducing a the number of models to be matched in a set of potential subterranean formation models.

FIELD

The present application relates to the field of reservoir modelling, andparticularly to methods, systems and devices for modellingunconventional oil reservoir production based on collected physicaldata.

BACKGROUND

Hydrocarbon exploration involves trade-offs between the number andspacing of wells (and associated costs) and the geological andcommercial risk based on available data which may impact productionforecasting and resource development planning.

Type curves can be used to estimate reservoir production for new wellsby averaging existing wells. However, in some instances, type curves maybe difficult to adjust for differences, and may not account for subtlechanges across an area or over time.

Simulations can also be used to model reservoir properties; however,simulations may require large amounts of input data which may beexpensive to obtain, and are expensive from both a time andcomputational resource perspective.

Methods, systems and devices which can reduce computational requirementsand/or input data requirements are desirable.

SUMMARY

In accordance with one aspect, there is provided a method of modellinghydrocarbon production rates for a subterranean formation. The methodincludes: obtaining, by at least one processor, production data for atleast one well in the subterranean formation; based at least in part ongeological data for the subterranean formation, identify, at the atleast one processor, a range of potential values for each of a pluralityof parameters, the plurality of parameters including at least oneparameter representative of geological characteristics of thesubterranean formation, and fracture parameters; where each set ofvalues including a selection from each of the ranges for the pluralityof parameters defining a potential subterranean formation model, andwhere sets of values including different combinations of values for theplurality of parameters define a set of potential subterranean formationmodels; matching at least a portion of the set of potential subterraneanformation models to the production data for the at least one well byiteratively: inputting, by the at least one processor, a set ofparameter values selected from the ranges of potential values to ananalytical fracture model to generate a production model for thesubterranean formation for the particular subterranean formation modeldefined by the inputted set of values, the production model a functionof a stimulated area value; determine at least one stimulated area valuefor the production model, and comparing production values for theproduction model with the production data for the at least one well togenerate an error value; and selecting parameter values for inputting ina subsequent iteration based on a machine learning algorithm and pasterror values to reduce a number of analyzed subterranean formationmodels that do not fit the production profile; identifying productionmodels which fit the production profile from the production data withina defined error threshold; with the identified production models whichfit the production profile from the production data for the at least onewell in the subterranean formation, selecting a range of stimulated areavalues from a subset of the identified models having the lowestgenerated error values; and based on a frequency distribution of thestimulated area values from the subset of the identified models havingthe lowest productivity value error scores, creating a forecastproduction model for at least a portion of the subterranean resource,the forecast production model having input parameters representative ofgeological characteristics of at least the portion of the subterraneanformation, and an input parameter associated with the stimulated areavalue and limited to the selected range.

In accordance with another aspect, there is provided a system formodelling hydrocarbon production rates for a subterranean formation. Thesystem includes at least one processor configured for: obtainingproduction data for at least one well in the subterranean formation;based at least in part on geological data for the subterraneanformation, identify a range of potential values for each of a pluralityof parameters, the plurality of parameters including at least oneparameter representative of geological characteristics of thesubterranean formation, and fracture parameters; where each set ofvalues including a selection from each of the ranges for the pluralityof parameters defining a potential subterranean formation model, andwhere sets of values including different combinations of values for theplurality of parameters define a set of potential subterranean formationmodels; matching at least a portion of the set of potential subterraneanformation models to the production data for the at least one well byiteratively: inputting a set of parameter values selected from theranges of potential values to an analytical fracture model to generate aproduction model for the subterranean formation for the particularsubterranean formation model defined by the inputted set of values, theproduction model a function of a stimulated area value; determine atleast one stimulated area value for the production model, and comparingproduction values for the production model with the production data forthe at least one well to generate an error value; and selectingparameter values for inputting in a subsequent iteration based on amachine learning algorithm and past error values to reduce a number ofanalyzed subterranean formation models that do not fit the productionprofile; identifying production models which fit the production profilefrom the production data within a defined error threshold; with theidentified production models which fit the production profile from theproduction data for the at least one well in the subterranean formation,selecting a range of stimulated area values from a subset of theidentified models having the lowest generated error values; and based ona frequency distribution of the stimulated area values from the subsetof the identified models having the lowest productivity value errorscores, creating a forecast production model for at least a portion ofthe subterranean resource, the forecast production model having inputparameters representative of geological characteristics of at least theportion of the subterranean formation, and an input parameter associatedwith the stimulated area value and limited to the selected range.

In accordance with another aspect, there is provided a computer-readablemedium or media having stored thereon computer-readable instructionswhich when executed by at least one processor configured the at leastone processor for: obtaining, by the at least one processor, productiondata for at least one well in the subterranean formation; based at leastin part on geological data for the subterranean formation, identify, atthe at least one processor, a range of potential values for each of aplurality of parameters, the plurality of parameters including at leastone parameter representative of geological characteristics of thesubterranean formation, and fracture parameters; where each set ofvalues including a selection from each of the ranges for the pluralityof parameters defining a potential subterranean formation model, andwhere sets of values including different combinations of values for theplurality of parameters define a set of potential subterranean formationmodels; matching at least a portion of the set of potential subterraneanformation models to the production data for the at least one well byiteratively: inputting, by the at least one processor, a set ofparameter values selected from the ranges of potential values to ananalytical fracture model to generate a production model for thesubterranean formation for the particular subterranean formation modeldefined by the inputted set of values, the production model a functionof a stimulated area value; determine at least one stimulated area valuefor the production model, and comparing production values for theproduction model with the production data for the at least one well togenerate an error value; and selecting parameter values for inputting ina subsequent iteration based on a machine learning algorithm and pasterror values to reduce a number of analyzed subterranean formationmodels that do not fit the production profile; identifying productionmodels which fit the production profile from the production data withina defined error threshold; with the identified production models whichfit the production profile from the production data for the at least onewell in the subterranean formation, selecting a range of stimulated areavalues from a subset of the identified models having the lowestgenerated error values; and based on a frequency distribution of thestimulated area values from the subset of the identified models havingthe lowest productivity value error scores, creating a forecastproduction model for at least a portion of the subterranean resource,the forecast production model having input parameters representative ofgeological characteristics of at least the portion of the subterraneanformation, and an input parameter associated with the stimulated areavalue and limited to the selected range.

Many further features and combinations thereof concerning embodimentsdescribed herein will appear to those skilled in the art following areading of the present disclosure.

DESCRIPTION OF THE FIGURES

In the figures,

FIG. 1 is a cross sectional view of an example geological formation andwell;

FIG. 2 is an example system to which aspects of the present disclosuremay be applied;

FIG. 3 is a perspective sectional view of an example horizontal wellportion with fractures;

FIG. 4 is a top view of an example horizontal well portion withfractures;

FIGS. 5, 6 and 7 are flowcharts illustrating aspects of example methodsfor modelling reservoir properties;

FIGS. 8 and 9 is are stimulated area vs. error value plots;

FIG. 10 shows an example geographic map showing different productionforecasts for different portions of a resource; and

FIG. 11 shows a graph showing examples of different probabilisticforecasts of production rates.

DETAILED DESCRIPTION

In hydrocarbon development, accurate estimations of rates of productioncan help provide information regarding the value and/or viability of aproject/resource. These estimations may also guide the number, locationand/or orientation of wells. Due to the high cost of development, therecan be significant financial incentives to properly describe uncertaintyin outcomes so informed decisions can be made as much as possible. Insome examples, it may be important to keep the cost and amount of timespent acquiring the information low.

In some embodiments, aspects of the present disclosure may provideanalytic devices, systems and methods for modelling resource productionwhich are computationally less intensive or less time consuming than acomplex simulation. In some embodiments, aspects of the presentdisclosure may have a higher degree of confidence in their models than atype curve or other similar model.

In some embodiments, aspects of the present disclosure may providedevices, systems and methods for modelling resource production based onincomplete or less information than would be necessary for otherprocesses.

In broad embodiments, aspects of the disclosure may, in some instances,provide a practical method for spatially modelling value to target areasof highest potential investment return.

FIG. 1 illustrates a cross-sectional view of a subterranean resource orgeological formation 110 which may include a number of different layersof materials having different physical characteristics as illustrated inFIG. 1 by the lines in the formation. It should be understood that theselines are illustrative only and that geological formations may have anynumber of layers or types of material which may not have distinctdelineations but may be gradual or may contain mixtures or combinationsof different material. There may also be lateral and/or verticalvariations in the types of material contained within any of thegeological formations.

In evaluating the subsurface or subterranean formations, in someexamples, data is collected from one or more wells 100 drilled into oraround the formations. In some examples, the wells are exploratorywells, production wells or wells for any other purpose. The wells mayinclude vertical wells 100, horizontal wells 105, or any wells of anydirection or structure, and/or any combination thereof.

In some examples, data collected from the well(s) 100 can include or canbe used to create logs of the geologic formations penetrated by thewell(s). The data can be collected from core samples or by measurementstaken by devices in the borehole.

In some examples, the well data collected or generated from wellmeasurements can include, but are not limited to, gamma ray logs, bulkdensity logs, neutron density logs, induction resistivity logs, and/orwell core or image data.

In some examples, the geological formation may includehydrocarbon-bearing layers having low permeability such as shale ortight sandstone. Such formations may be suitable for hydrocarbonextraction using hydraulic fracturing technologies. In some instances,such unconventional plays may have large spatial variability, mayinvolve multiple hydrocarbon fluids phases, and/or may haveuncertainties in fracturing areas and permeability.

As such, in some instances, traditional techniques for conventional oilwell drilling may be unsuitable for these unconventional resources.

The embodiments of the devices, systems and methods described herein maybe implemented in a combination of both hardware and software. Theseembodiments may be implemented on programmable computers, each computerincluding at least one processor, a data storage system (includingvolatile memory or non-volatile memory or other data storage elements ora combination thereof), and at least one communication interface.

Program code may be applied to input data to perform the functionsdescribed herein and to generate output information. The outputinformation may be applied to one or more output devices. In someembodiments, the communication interface may be a network communicationinterface. In embodiments in which elements may be combined, thecommunication interface may be a software communication interface, suchas those for inter-process communication. In still other embodiments,there may be a combination of communication interfaces implemented ashardware, software, and combination thereof. In some examples, deviceshaving at least one processor may be configured to execute softwareinstructions stored on a computer readable tangible, non-transitorymedium.

The following discussion provides many example embodiments. Althougheach embodiment represents a single combination of inventive elements,other examples may include all possible combinations of the disclosedelements. Thus if one embodiment comprises elements A, B, and C, and asecond embodiment comprises elements B and D, other remainingcombinations of A, B, C, or D, may also be used.

The technical solution of embodiments may be in the form of a softwareproduct. The software product may be stored in a non-volatile ornon-transitory storage medium, which can be a compact disk read-onlymemory (CD-ROM), a USB flash disk, or a removable hard disk. Thesoftware product includes a number of instructions that enable acomputer device (personal computer, server, or network device) toexecute the methods provided by the embodiments.

The embodiments described herein are implemented by physical computerhardware, including computing devices, servers, receivers, transmitters,processors, memory, displays, and networks. The embodiments describedherein provide useful physical machines and particularly configuredcomputer hardware arrangements. The embodiments described herein aredirected to electronic machines and methods implemented by electronicmachines adapted for processing and transforming electromagnetic signalswhich represent various types of information. The embodiments describedherein pervasively and integrally relate to machines, and their uses;and the embodiments described herein have no meaning or practicalapplicability outside their use with computer hardware, machines, andvarious hardware components. Substituting the physical hardwareparticularly configured to implement various acts for non-physicalhardware, using mental steps for example, may substantially affect theway the embodiments work. Such computer hardware limitations are clearlyessential elements of the embodiments described herein, and they cannotbe omitted or substituted for mental means without having a materialeffect on the operation and structure of the embodiments describedherein. The computer hardware is essential to implement the variousembodiments described herein and is not merely used to perform stepsexpeditiously and in an efficient manner.

FIG. 2 shows an example system 200 include one or more devices 205 whichmay be used to model or predict hydrocarbon production rates. In someexamples, a device 205 may be a computational device such as a computer,server, tablet or mobile device, or other system, device or anycombination thereof suitable for accomplishing the purposes describedherein. In some examples, the device 205 can include one or moreprocessor(s) 210, memories 215, and/or one or more devices/interfaces220 necessary or desirable for input/output, communications, control andthe like. The processor(s) 210 and/or other components of the device(s)205 or system 250 may be configured to perform one or more aspects ofthe processes described herein.

In some examples, the device(s) 205 may be configured to receive oraccess data from one or more volatile or non-volatile memories 215, orexternal storage devices 225 directly coupled to a device 205 oraccessible via one or more wired and/or wireless network(s) 260. Inexternal storage device(s) 225 can be a network storage device or may bepart of or connected to a server or other device.

In some examples, the data may be accessed from one or more publicdatabases. Such data can, in some examples, include less wellcharacteristic and/or production data than may be available for welldata from an internal source. For example, well production data may beprovided as an aggregate of multiple wells or for an area without anyinformation as to the number or size of fractures. In another example,well production data may be provided over time in less granular timeperiods. In some embodiments, the methods, devices, and systemsdescribed herein may generate models which account for such unknown(s).

In some examples, the device(s) 205 may be configured to receive oraccess data from sensors or devices 230 in the field. These sensors ordevices 230 may be configured for collecting or measuring well, seismicor other geological and/or physical data. In some examples, thesensor(s)/device(s) 230 can be configured to communicate the collecteddata to the device(s) 205 and/or storage device(s) 225 via one or morenetworks 260 or otherwise. In some examples, the sensors or devices 230may be connected to a local computing device 240 which may be configuredto receive the data from the sensors/devices 230 for local storageand/or communication to the device(s) 205 and/or storage device(s) 225.

In some examples, a client device 250 may connect to or otherwisecommunicate with the device(s) 205 to gain access to the data and/or toinstruct or request that the device(s) 205 perform some or all of theaspects described herein.

With reference to FIG. 3, in some embodiments, a well may have multiplehydraulic fractures 310, which may be transverse or in any otherorientation with respect to the well. The wellbore 120 in FIG. 3 ishorizontal; however, in other examples, fractures can be made relativeto a wellbore of any orientation.

FIG. 4 shows a top-down view of the horizontal well 120 including fourfractures 310. In some embodiments, a well with multiple fractures canbe modelled as equally-spaced bi-wing transverse fractures. In someembodiments, the model can assume that there is a no flow boundary 315at a midpoint between each fracture.

On the right, FIG. 4 shows an example drainage area for a singlefracture 310. In some embodiments, fracture parameters can include anumber of fractures, a fracture drainage area half-length Y_(e), afracture drainage area half width X_(e), a fracture half-length X_(f),and the like.

In some examples, the system can be configured to treat each fracture ofa multi-fracture well as multiple wells with a single fracture each. Insome instances, this may simplify the models and may reduce thecomputational load on the system.

The model can account for spatial differences in geology throughgeostatistical realization. Multiple models are run on a finite anddiscrete number of areas with a larger defined region. Distributions canthen be calculated for each area. The model can represent one regionover a play or can be run on several.

FIG. 5 shows a flowchart illustrating aspects of an example method 500for modelling hydrocarbon production rates for a subterranean formation.At 510, one or more processor(s) 210 and/or other aspects of device(s)205 may be configured to receive, access, compile or otherwise obtainproduction data for at least one well in the subterranean formation 110.

In some examples, the production data can be obtained from one or morememories 215, storage devices 215, 225, and/or sensors or field devices230, 240. In some examples, the production data can include periodic(e.g. daily, weekly, monthly, etc.) production values, cumulativeproduction values or any other data values from which suitableproduction data can be calculated.

In some embodiments, the production data for the well(s) should span atleast 6 months of normalized production in order to produce meaningfulresults.

The processor(s) can also obtain drilling data, completion data, and/ordata associated with geological properties.

In some examples, data associated with geological properties can includewell logs such as gamma ray well log(s), bulk density well log(s),neutron density well log(s), resistivity well log(s), core and/or wellimage data, nuclear magnetic resonance log(s), and/or any other well logthat can be measured in the well.

In some examples, the processor(s) drilling and/or completion data caninclude fracture heights, fracture half lengths, a number of fractures,a fracture drainage area half-lengths, a fracture drainage area halfwidths, a fracture half-lengths, well lengths, and the like.

In some embodiments, data may be obtained from internal data sources, ordata collected from drilled wells and fracturing processes.

In some embodiments, data may be obtained from public sources such as adata retrieved from a government or otherwise public fracturingdatabase. This public data may include production data for whichproduction values for multiple fractures and/or wells may be combinedinto a single value. In some examples, the public data may not includeall fracture characteristics or geological data.

In accordance with some embodiments, the methods, systems and devicesherein may accommodate for incomplete data sources such as public dataor limited confidential data from a third party while still providing aproduction model with a reasonable degree of confidence.

In some embodiments, the processor(s) may combine internal and externaldata sources.

At 520, the processor(s) identify a range of values for each parameterin a set of parameters for the subterranean formation. In some examples,the range of values for a parameter can be identified by determining apossible range of values based on geological data. In some embodiments,the processors can receive or otherwise obtain ranges of values from oneor more input sources which may be based at least in part on thecollected geological data for the subterranean formation.

The set of parameters can include one or more geological parametersrepresentative of geological characteristics of the subterraneanformation. For example, geological parameters can include one or more offormation height, reservoir depth, porosity, permeability, watersaturation, and the like. In some examples, the geological parameterscan include pressure properties, and/or rock and fluid propertiesincluding, for example, pressure gradient, initial pressure, operatingconditions such as early or late well flowing pressure, months to wellflowing pressure change, temperature gradient, reservoir temperature,rock compressibility, water compressibility, API (American PetroleumInstitute) gravity, gas-to-oil ratio, combined gas gravity, relative gaspermeability, residual gas saturation, critical gas saturation, gasviscosity, condensate gas ratio and the like.

In some examples, the set of parameters can include well parameters suchas completion parameters and fracture parameters. These parameters caninclude fracture heights, fracture half lengths, a number of fractures,fracture drainage area half-lengths, fracture drainage area half widths,fracture half-lengths, well lengths, and the like.

In some instances, one or more parameters may be fixed or constant basedon the parameter itself or the obtained data. These parameter(s) willhave a single value. However, other parameters may be unknown or may notbe pinpointed exactly, so the processor(s) generate or receive a rangeof potential values for the parameter(s). These ranges can be based onthe obtained geological and/or other obtained data.

For example, the processor(s) can generate or receive parameter rangeswhich would be reasonable or possible based on log data, geostatisticalmodels and/or extrapolated data between wells. In some examples, theprocessor(s) can generate or receive parameter ranges based oncorrelations with other parameters. For example, pressure(s) may becorrelation with reservoir depth. In some examples, the range of valuesmay be based on correlations with other geological formations havingsimilar geological data.

In some embodiments, the processor(s) can generate or receive agranularity or increment by which the ranges of parameter values can bevaried in the system.

Each combination of values including a selection from each range for theset of parameters corresponds to, defines or otherwise represents apotential subterranean formation model, and the total set of differentcombinations of values for the set of parameters defines a set ofpotential subterranean formation models.

At 530, the processor(s) match the set of potential subterraneanformation models to the production data for the well(s). The matching isbased on an analytical fracture model. In some examples, the analyticalfracture model can generate a production model based on the geologicalparameters. However, as described herein, the base analytical model caninclude a number of unknowns which cannot be solved directly. In someembodiments, a number of these unknowns can be combined into a singlestimulated area value. In some examples, the stimulated area value canbe based on a number of parameters in the set of parameters defining orotherwise associated with properties of a subterranean formation model.

In some examples, using a combination of values for the set ofparameters as inputs to the analytical fracture model, the processor(s)can generate a production model for the potential subterranean formationmodel corresponding to the set of input values. In some examples, theprocessor(s) can determine a stimulated area value for the generatedproduction model.

The processor(s) compare the generated production model with theproduction data from the well(s) to generate an error value between theproduction of the generated model and the physical well production data.In some examples, the error value may be a total error over theproduction period, an average error, a maximum error, or any other errormetric. In some embodiments, the error value may be based on individualproduction values for each time period.

In some embodiments, the error value may be based on one or more ofcumulative gas production, gas production rate, cumulative oilproduction, oil production rate, and the like.

In some embodiments, the processor(s) are configured to select parametervalues for inputting in a subsequent iteration based on a machinelearning algorithm and previous error values. In some examples, theprocessor(s) can be configured to use a genetic algorithm to selectsubsequent parameter values for generating subsequent models.

In some embodiments, the genetic algorithm can optimize or improve thesearching of a large solution space. It can include selecting severalsets of random values from all parameters and solving for the objectivematching function. The results which provide the best matching functionresult can be merged together to find new sets of values for testing.This process is iterated with the best matching function results fromeach iteration used in subsequent sets of values for testing. Inaddition to or alternatively to previous inputs sets being combined, insome embodiments, random variations can be introduced to input sets. Insome instances, this can reduce the chance of solutions converging on alocal optimal rather than a global optimal.

In some instances, this may reduce the number of models to be analyzed,and may reduce the computation time and resources required to completethe model matching process.

At 540, the processor(s) identify the models from the set of potentialsubterranean formation models which fit the production profile from theproduction data within a defined error threshold. In some examples, thisincludes identifying the models having an error value less than thedefined error threshold. In some examples, the error threshold may be astatically defined threshold. In other examples, the error threshold maybe based on a defined percentile of the models.

In some embodiments, the error at different stages of production can beweighted differently. For example, if early production results are moreimportant, the error for earlier stages of production can be weightedmore than error for later stages of production; and vice versa. Theseweightings can be applied to objective matching functions.

In some embodiments, the determination of the stimulated area valuesincludes performing two runs to deliver a stable region. On the firstrun, a consistent number (e.g. 5000) of trials are performed on eachrun. On the second run, the model can be rerun with the last goodsolution as a starting point to ensure tight clustering of values. Againa consistent number of runs should be used. In some embodiments, threecriteria are then used to define an acceptable solution space. First, aminimum absolute error of at least 20% should be achieved for a run tobe considered valid. All runs should be completed with similar weightingto ensure the results are comparable. Second, the mean error can beexamined as it progresses through the solution space. Cases that arewithin a best fit mean error will be retained. Only trials with adeviation of less than 1% will be used. Third, the maximum error of 2×the minimum error should be used to bound the cases. The correspondingtotal error for this stable region of running average stimulated areavalue can be used to pick a minimum and maximum stimulated area value.In other embodiments, different mechanisms for determining thestimulated area values may be used.

At 550, the processor(s) select a range of stimulated area values fromthe identified models which fit the production profile from theproduction data within the defined error threshold. In some examples,the selected range is based on the models having the lowest errorvalues. In some examples, the selected range is based on a concentrationof stimulated area values which correspond to models having a low errorvalue.

At 560, the processor(s) create a forecast production model for thesubterranean resource having inputs based on the geological data, andstimulated value input(s) based on the selected range. The process forforecasting production model is described in the following sections.

Analytical Model

As described above, in some embodiments, the matching process at 530 isbased on an analytical fracture model. In some examples, the analyticalfracture model can involve a gas model, an oil model or both.

FIG. 6 shows an example flowchart 600 outlining aspects of an examplegas model. As described herein or otherwise, the processor(s) generateor receive physical input values or ranges of physical input valuesbased on obtained geological data. In some examples, such geologicaldata can be derived from petrophysical interpretation of well logs fromadjacent or nearby wells. In some embodiments, the geological data caninclude time steps, pressure differences (initial, early, late), netpay, gas permeability, porosity, drainage area half width, fracturespacing half distance, condensate gas ratio, and the like.

PARAMETER Units Min Max Increments Skin Shape 0.5 3 0.1 Function Krg 0.10.5 0.02 Formation Net m 53.24 70.69 0.25 Thickness Frac Height % 60%100%   2% Frac half length m 20 85 2 Well Length m 1200 1391 5 Number ofFracs Count 9 12 1 Reservoir Depth m 3236 3328 0 Pressure Gradientpsi/ft 0.759927 0.834638 0.01 Early Pwf psig 2000 7500.0 100 Late Pwfpsig 200 2000.0 20 Pwf Change Time Months 0 6.0 1 Temperature F/ft 0.020.03 0.001 Gradient Rock Compres- 1/psi 1.0E−07 6.0E−06 2.0E−07 sibilityPorosity %  5%  6% 0.1% Permeability mD −4 −2.52 0.01 (log scale) WaterSaturation % 10%  18% 0.25%  CGR Bbl/Mmcf 50.00 89.00 5.00

From the physical inputs, the processor(s) may calculate other inputswhich may be dependent or otherwise correlated with the physical inputsor other calculated inputs. These calculated inputs or correlations mayinclude gas z factor calculations, critical temperatures and pressuresfor miscellaneous gasses, gas viscosity correlations, gascompressibility correlations, gas pseudopressure miscellaneous gasses,temperature, skin, k slippage and the like. These calculations may beperformed with any currently known or future techniques.

The table above illustrates example physical and calculated inputs whichmay be used to create models for the subterranean formation.

Based on Darcy's Law, in its simplest form, radial flow q is based onboth an effective permeability, and a fracture area:

$q = \frac{{kA}*\Delta \; p}{\mu*L}$

Assuming all other factors are constant, if permeability increases, thefracture area must be lower to achieve the same flow rate. Since theseparameters are both unknown, the relationship between these parameterscan be determined to select appropriate forecast models which willproduce accurate results. These unknowns can be combined into astimulated area value which may be solved based on the known productiondata.

In a simplified linear flow equation:

$\frac{1}{q} = {{m\sqrt{t}} + b^{\prime}}$

Oil and gas flow equations are different:

$m = {\frac{31.3B}{{hx}_{f}\sqrt{k}}\sqrt{\frac{\mu}{\varnothing \; c_{t}}}*\frac{1}{p_{i} - p_{wf}}}$

Oil:

$m = {\frac{315.4T}{h\sqrt{\varnothing \; \mu_{g}c_{t}}}*\frac{1}{p_{i} - p_{wf}}*\frac{1}{x_{f}\sqrt{k}}}$

Gas:

As highlighted these linear flow equations share the unknowns of paythickness h, the fracture half-width x_(f), and the square root of thepermeability k. In some embodiments, processor(s) can be configured tocombine these into a single stimulated area value. This stimulated areavalue can, in some embodiments, be the stimulated area A (h*x_(f)) timesthe root of the effective permeability k.

In some embodiments, the analytical model for gas may be based on anequivalent gas flow rate equation:

$\begin{matrix}{{q_{g} = \frac{({skin})( {\# \mspace{14mu} {of}\mspace{14mu} {fracs}} )( {\Delta \; p} )(h)( K_{gas} )}{( {{Gas}\mspace{14mu} {Constant}} )( {460 + T} )( P_{{wd}\; \frac{Gas}{Frac}} )}}{Where}{{skin} = {{permeability}\mspace{14mu} {adjustment}\mspace{14mu} {factor}\mspace{14mu} {due}\mspace{14mu} {to}\mspace{14mu} {liquid}\mspace{14mu} {drop}\mspace{14mu} {out}}}{{\Delta \; p} = {{difference}\mspace{14mu} {in}\mspace{14mu} {pressure}\mspace{14mu} {across}\mspace{14mu} {wellface}}}{h = {{pay}\mspace{14mu} {thickness}}}{K_{gas} = {{gas}\mspace{14mu} {permeability}}}{T = {{reservoir}\mspace{14mu} {temperature}\mspace{14mu} {in}\mspace{14mu} {degrees}\mspace{14mu} {Farenheit}}}{P_{{wd}\; \frac{Gas}{Frac}} = {{dimensionless}\mspace{14mu} {pressure}}}} & (1)\end{matrix}$

The dimensionless pressure can be based on a Gringarten (Gringarten, A.C., Ramey, H. J., “Unsteady-State Pressure Distributions created by awell with a single Infinite-Conductivity Vertical Fracture”, StanfordUniversity, August 1974) approach using dimensionless time:

$\begin{matrix}{{{Tda}\mspace{14mu} {Gas}} = \frac{0.00633*K_{gas}*{Green}\mspace{14mu} {Function}\mspace{14mu} {Time}}{\mu_{g}*\varnothing*C_{t_{Gas}}*4*X_{e}*Y_{e}}} & (2)\end{matrix}$

Where

-   -   μ_(g)=gas viscosity    -   Ø=porosity    -   C_(t) _(Gas) =gas compressability    -   Xe=drainage area half width, and    -   Ye=drainage area half-length or half distance between fracs

With equation (2), the processor(s) can generate a log of dimensionlesstime values. In some examples, this model may assume and treat eachfracture as a single vertical well with a single horizontal fracture. Insome embodiments, the processor(s) handle each fracture in a well withmultiple fractures as individual identical single fracture wells with awell length based on the original well length divided by the number offractures.

Based on the above and using Green Equations, the processor(s) cangenerate an analytical model including a log of dimensionless time andpressure estimates. From these logs and equation (1), a single phase gasforecast estimate can be provided for each time step. These cumulativegas volumes are at surface conditions prior to liquids being removed.

The relationship of pressure drop over time p/z can be used to calculatepressure steps as the gas is produced. In some embodiments, theprocessor(s) generate the p/z relationship based on initial pressure,and final pressure from the measured or calculated data. For example, aninitial pressure can be a known measured data point, or it can becalculated based on depth and gradient data. In some examples, thegradient may be a varied parameter during the matching process.

Based on iterations of:

${{P/Z}\mspace{14mu} {slope}} = \frac{{Pwf} - {Pi}}{Qg}$

the pressures at each interval can be generated.

In some embodiments, each time interval can be divided into two or moresubintervals. The processor(s) can be configured to determine thepressure, P/Z slope and Q for each subinterval. The average pressureacross these subintervals is then used as the pressure for the wholeinterval. In some examples, this can potentially provide a more accurateestimation of the changing pressure as the well ages.

In some embodiments, the processor(s) can be configured to account forchanges to the gas/liquid composition changes with pressure. Based onthe condensate gas ratio parameter, the processor(s) can generate oraccess a database of PVT (pressure-volume-temperature) tables atdifferent yield bands.

In addition to the analytical model for gas production, in someembodiments, the processor(s) can generate an analytical model whichalternatively or additional accounts for oil production. FIG. 7 shows anexample flowchart 700 outlining aspects of an example oil model. Asdescribed herein or otherwise, the processor(s) generate or receivephysical input values or ranges of physical input values based onobtained geological data. In some examples, such geological data can bederived from petrophysical interpretation of well logs from adjacent ornearby wells. In some embodiments, the physical inputs can include timesteps, pressure differences, net pay, effective permeability, porosity,drainage area half width, fracture spacing half distance, condensate gasratio or gas oil ratio, initial water saturation and the like.

From the physical inputs, the processor(s) may calculate other inputswhich may be dependent or otherwise correlated with the physical inputsor other calculated inputs. These calculated inputs or correlations mayinclude oil viscosity, gas viscosity, oil expansion factor, gasexpansion factor, bubble point pressure, oil compressibility, formationvolume factors, solution gas-oil ratio, formation volume factor, oilexpansion factor, and the like. In some examples, these calculatedinputs may be calculated relative to a bubble point pressure. Thesecalculations may be performed with any currently known or futuretechniques.

As described above, the processor(s) can generate the oil analyticalmodel by determining a stimulated area value (e.g. A root K) similar tothe gas model. However, the dimensionless time value function for oilcan be based on:

${{Tda} = \frac{0.00633*K_{oil}*{Green}\mspace{14mu} {Function}\mspace{14mu} {Time}}{\mu_{o}*\varnothing*C_{t}*4*( {( {X_{e}*Y_{e}} )/(0.3048)^{2}} )}},{and}$$q_{o} = \frac{( {\# \mspace{14mu} {of}\mspace{14mu} {fracs}} )( {\Delta \; p} )(h)( k_{eff} )( k_{ro} )}{(141.2)( \mu_{o} )( P_{wd} )( B_{ti} )}$

Where

-   -   Tda=dimensionless time    -   Δp=difference in pressure across wellface    -   h=pay thickness or layer thickness*frac height    -   K_(eff)=absolute effective permeability    -   K_(oil)=relative permeability to oil    -   P_(wd)=dimensionless pressure    -   μ_(o)=gas viscosity    -   C_(t)=gas compressability    -   Xe=drainage area half width    -   Ye=drainage area half-length or half distance between fracs    -   # of fracs=number of fractures in the horizontal well    -   Bti=Total expansion factor

Based on the above and using Green Equations, the processor(s) cangenerate an analytical oil model including a log of dimensionless timeand pressure estimates. From these logs and equations, an oil forecastestimate can be provided for each time step. These cumulative gasvolumes are at surface conditions prior to liquids being removed.

In some embodiments, the processor(s) can apply material balanceequations to adjust the oil production model to account for differentgas-oil ratios at different pressures.

Absolute permeability is the measure of the ability of a single phasefluid to move through a porous medium. When multiple phases (ie. Gas andoil, or oil and water) are present at the same time inefficiencies arecreated resulting in a permeability that is a fraction of the absolutepermeability. This is referred to as relative permeability. Relativepermeability changes as a function of the saturation of one phase as apercentage of pore volume. Relative permeability curves describe thisrelationship. The curves can be determined through special core analysisor assumed based on an analog. In the oil production model, relativeperm can be used to account for changes in productivity as the reservoiris depleted and gas is introduced out of solution. The relativepermeability adjustment causes an appropriate reduction in productivity.

Well Matching

As discussed above, the processor(s) match the set of potentialsubterranean formation models to the production data for the well(s)based on an analytical fracture model. In some embodiments, theprocessor(s) can match the potential subterranean formation models basedon both an oil analytical fracture model and a gas analytical fracturemodel. In some embodiments, each model can produce its own productionmodels and associated stimulated area values. In some examples, theprocessor(s) can use the results of the two different models (gas oroil) to determine a probability that a portion or all of a subterraneanformation will use one model over the other.

After matching the models, the processor(s) can store and/or compile allthe production models and their corresponding error values andstimulated area values. FIG. 8 shows a plot 800 of stimulated area vs.error with each data point representing a matched production model. Insome examples, the processor(s) can be configured to generate such aplot and output it on an output device such as a display, printer, orcommunication device.

The processor(s) can be configured to identify a subset 810 of theproduction models (see FIGS. 8 and 9) which have an error value below adefined threshold or which otherwise fit the production profile from theproduction data within a defined error threshold.

Forecasting Model

At 560, the processors generate a forecast production model. In someembodiments, the forecast production model is defined by a number ofinput parameters representative of geological characteristics of thesubterranean formation. The forecast production model is based on thestimulated area values identified by the analytical model and wellmatching.

By applying distributions of reservoir input parameters for the area ofinterest, the forecast production model can generate productionforecasts over time for the area of interest. In some embodiments,ranges and/or distributions of input parameters for the area of interestcan be used as inputs to generate an average production forecast for thearea.

In some embodiments, the forecasting model can be run deterministicallyusing single values for each parameter or Monte Carlo or similartechniques can be used to deliver a distribution of productionforecasts. Forecasts can be created for both hydrocarbon liquids andgas.

In some embodiments, the forecast models can provide an indication ofpredicted average production rates over time. In other embodiments, theforecast models can provide probabilistic production rates based on thepossible distributions for input parameters including the geologicalcharacteristics and the stimulated area value. As illustrated in FIG.11, in some embodiments, graphs are generated to illustrated differentprobabilistic production rates over time.

In some embodiments, by applying input parameters representative ofgeological characteristics of a particular area or localized region, thesystem can, in some instance, model production rates which account forphysical and potentially subtle geological variations across an area.

As illustrated in FIG. 10, in some embodiments, forecast models can beused to generate a visual map illustrating different productionforecasts across a prospective area. In some instances, the forecastmodels can be used to generate a probabilistic financial viabilities ofdifferent portions of an area.

As described herein, in some embodiments, these forecast models can insome instances account for various unknowns in the available productiondata and/or variations in geological characteristics across a play.

Although the embodiments have been described in detail, it should beunderstood that various changes, substitutions and alterations can bemade herein without departing from the scope as defined by the appendedclaims.

Moreover, the scope of the present application is not intended to belimited to the particular embodiments of the process, machine,manufacture, composition of matter, means, methods and steps describedin the specification. As one of ordinary skill in the art will readilyappreciate from the disclosure of the present invention, processes,machines, manufacture, compositions of matter, means, methods, or steps,presently existing or later to be developed, that perform substantiallythe same function or achieve substantially the same result as thecorresponding embodiments described herein may be utilized. Accordingly,the appended claims are intended to include within their scope suchprocesses, machines, manufacture, compositions of matter, means,methods, or steps

As can be understood, the examples described above and illustrated areintended to be exemplary only. The scope is indicated by the appendedclaims.

What is claimed is:
 1. A method of modelling hydrocarbon productionrates for a subterranean formation, the method comprising: obtaining, byat least one processor, production data for at least one well in thesubterranean formation; based at least in part on geological data forthe subterranean formation, identify, at the at least one processor, arange of potential values for each of a plurality of parameters, theplurality of parameters including at least one parameter representativeof geological characteristics of the subterranean formation, andfracture parameters; where each set of values including a selection fromeach of the ranges for the plurality of parameters defining a potentialsubterranean formation model, and where sets of values includingdifferent combinations of values for the plurality of parameters definea set of potential subterranean formation models; matching at least aportion of the set of potential subterranean formation models to theproduction data for the at least one well by iteratively: inputting, bythe at least one processor, a set of parameter values selected from theranges of potential values to an analytical fracture model to generate aproduction model for the subterranean formation for the particularsubterranean formation model defined by the inputted set of values, theproduction model a function of a stimulated area value; determining atleast one stimulated area value for the production model, and comparingproduction values for the production model with the production data forthe at least one well to generate an error value; and selectingparameter values for inputting in a subsequent iteration based on amachine learning algorithm and past error values to reduce a number ofanalyzed subterranean formation models that do not fit the productionprofile; identifying production models which fit the production profilefrom the production data within a defined error threshold; with theidentified production models which fit the production profile from theproduction data for the at least one well in the subterranean formation,selecting a range of stimulated area values from a subset of theidentified models having the lowest generated error values; and based ona frequency distribution of the stimulated area values from the subsetof the identified models having the lowest productivity value errorscores, creating a forecast production model for at least a portion ofthe subterranean resource, the forecast production model having inputparameters representative of geological characteristics of at least theportion of the subterranean formation, and an input parameter associatedwith the stimulated area value and limited to the selected range.
 2. Themethod of claim 1, wherein the stimulated area value is a function ofpermeability and fracture area.
 3. The method of claim 1, wherein theanalytical fracture model is a function of the stimulated area value. 4.The method of claim 1, wherein the analytical fracture model includesdimensionless time and dimensionless pressure logs to generate theproduction model for a series of time steps.
 5. The method of claim 1wherein the production data is collected over a period of time.
 6. Themethod of claim 1 wherein the geological data for the subterraneanformation is collected from at least one sensing device or apetrophysical analysis of well logs.
 7. The method of claim 1 whereinidentifying the range of potential values for each of a plurality ofparameters comprises identifying a granularity at which values can beselected within the range of potential values.
 8. The method of claim 1wherein the fracture parameters include parameters associated with anumber of fractures and at least one fracture area dimension.
 9. Themethod of claim 1 comprising: creating forecast models of differentportions of the subterranean resource, each forecast production modelhaving input parameters representative of geological characteristics ofthe respective portion of the subterranean formation.
 10. The method ofclaim 9 comprising: using the forecast models, generating a visual mapillustrating different production forecasts for the different portionsof the subterranean formation.
 11. A system for modelling hydrocarbonproduction rates for a subterranean formation, the system comprising atleast one processor configured for: obtaining production data for atleast one well in the subterranean formation; based at least in part ongeological data for the subterranean formation, identify a range ofpotential values for each of a plurality of parameters, the plurality ofparameters including at least one parameter representative of geologicalcharacteristics of the subterranean formation, and fracture parameters;where each set of values including a selection from each of the rangesfor the plurality of parameters defining a potential subterraneanformation model, and where sets of values including differentcombinations of values for the plurality of parameters define a set ofpotential subterranean formation models; matching at least a portion ofthe set of potential subterranean formation models to the productiondata for the at least one well by iteratively: inputting a set ofparameter values selected from the ranges of potential values to ananalytical fracture model to generate a production model for thesubterranean formation for the particular subterranean formation modeldefined by the inputted set of values, the production model a functionof a stimulated area value; determining at least one stimulated areavalue for the production model, and comparing production values for theproduction model with the production data for the at least one well togenerate an error value; and selecting parameter values for inputting ina subsequent iteration based on a machine learning algorithm and pasterror values to reduce a number of analyzed subterranean formationmodels that do not fit the production profile; identifying productionmodels which fit the production profile from the production data withina defined error threshold; with the identified production models whichfit the production profile from the production data for the at least onewell in the subterranean formation, selecting a range of stimulated areavalues from a subset of the identified models having the lowestgenerated error values; and based on a frequency distribution of thestimulated area values from the subset of the identified models havingthe lowest productivity value error scores, creating a forecastproduction model for at least a portion of the subterranean resource,the forecast production model having input parameters representative ofgeological characteristics of at least the portion of the subterraneanformation, and an input parameter associated with the stimulated areavalue and limited to the selected range.
 12. The system of claim 11,wherein the stimulated area value is a function of permeability andfracture area.
 13. The system of claim 11, wherein the analyticalfracture model is a function of the stimulated area value.
 14. Thesystem of claim 11, wherein the analytical fracture model includesdimensionless time and dimensionless pressure logs to generate theproduction model for a series of time steps.
 15. The system of claim 11wherein the production data is collected over a period of time.
 16. Thesystem of claim 11 wherein the geological data for the subterraneanformation is collected from at least one sensing device or apetrophysical analysis of well logs.
 17. The system of claim 11 whereinidentifying the range of potential values for each of a plurality ofparameters comprises identifying a granularity at which values can beselected within the range of potential values.
 18. The system of claim11 wherein the fracture parameters include parameters associated with anumber of fractures and at least one fracture area dimension.
 19. Thesystem of claim 11 wherein the at least one processor is configured for:creating forecast models of different portions of the subterraneanresource, each forecast production model having input parametersrepresentative of geological characteristics of the respective portionof the subterranean formation.
 20. The system of claim 19 wherein the atleast one processor is configured for: using the forecast models,generating a visual map illustrating different production forecasts forthe different portions of the subterranean formation.
 21. Acomputer-readable medium or media having stored thereoncomputer-readable instructions which when executed by at least oneprocessor configured the at least one processor for: obtaining, by theat least one processor, production data for at least one well in thesubterranean formation; based at least in part on geological data forthe subterranean formation, identify, at the at least one processor, arange of potential values for each of a plurality of parameters, theplurality of parameters including at least one parameter representativeof geological characteristics of the subterranean formation, andfracture parameters; where each set of values including a selection fromeach of the ranges for the plurality of parameters defining a potentialsubterranean formation model, and where sets of values includingdifferent combinations of values for the plurality of parameters definea set of potential subterranean formation models; matching at least aportion of the set of potential subterranean formation models to theproduction data for the at least one well by iteratively: inputting, bythe at least one processor, a set of parameter values selected from theranges of potential values to an analytical fracture model to generate aproduction model for the subterranean formation for the particularsubterranean formation model defined by the inputted set of values, theproduction model a function of a stimulated area value; determining atleast one stimulated area value for the production model, and comparingproduction values for the production model with the production data forthe at least one well to generate an error value; and selectingparameter values for inputting in a subsequent iteration based on amachine learning algorithm and past error values to reduce a number ofanalyzed subterranean formation models that do not fit the productionprofile; identifying production models which fit the production profilefrom the production data within a defined error threshold; with theidentified production models which fit the production profile from theproduction data for the at least one well in the subterranean formation,selecting a range of stimulated area values from a subset of theidentified models having the lowest generated error values; and based ona frequency distribution of the stimulated area values from the subsetof the identified models having the lowest productivity value errorscores, creating a forecast production model for at least a portion ofthe subterranean resource, the forecast production model having inputparameters representative of geological characteristics of at least theportion of the subterranean formation, and an input parameter associatedwith the stimulated area value and limited to the selected range.